Теорема Дюбуа-Прайда

Òåîðåìà Äþáóà-Ïðàéäà
Ïóñòü A, B íå÷åòêèå ÷èñëà, è îïåðàöèè ñëîæåíèÿ, óìíîæåíèÿ, âû÷èòàíèÿ è
äåëåíèÿ îïðåäåëåíû ïî ïðèíöèïó ðàñøèðåíèÿ. Òîãäà:
1. A + B , A − B , A · B , A/B íå÷åòêèå ÷èñëà;
Òåîðåìà Äþáóà-Ïðàéäà
Ïóñòü A, B íå÷åòêèå ÷èñëà, è îïåðàöèè ñëîæåíèÿ, óìíîæåíèÿ, âû÷èòàíèÿ è
äåëåíèÿ îïðåäåëåíû ïî ïðèíöèïó ðàñøèðåíèÿ. Òîãäà:
1. A + B , A − B , A · B , A/B íå÷åòêèå ÷èñëà;
2. Âûïîëíÿåòñÿ
dA + Be = dAe + dBe
dA − Be = dAe − dBe
dA · Be = dAe · dBe
dA/Be = dAe/dBe.
Òåîðåìà Äþáóà-Ïðàéäà
Ïóñòü A, B íå÷åòêèå ÷èñëà, è îïåðàöèè ñëîæåíèÿ, óìíîæåíèÿ, âû÷èòàíèÿ è
äåëåíèÿ îïðåäåëåíû ïî ïðèíöèïó ðàñøèðåíèÿ. Òîãäà:
1. A + B , A − B , A · B , A/B íå÷åòêèå ÷èñëà;
2. Âûïîëíÿåòñÿ
dA + Be = dAe + dBe
dA − Be = dAe − dBe
dA · Be = dAe · dBe
dA/Be = dAe/dBe.
Z
|A| =
µA (a)ada
a∈R
Íå÷åòêèå îïåðàöèè
2
2,005
µ
1
2
x
Íå÷åòêèå îïåðàöèè
2
2,005
4
4,000
µ
1
2
4
x
Íå÷åòêèå îïåðàöèè
4
4,000
2+2
4,004
µ
1
4
x
Íå÷åòêèå îïåðàöèè
µ
4
4,000
2+2
4,004
2·2
4,620
1
4
x
Íå÷åòêèå îïåðàöèè
4
4,000
2+2
4,004
µ
2·2
4,620
1
8/2
5,456
4
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 1
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
2 4
4,000
2+2
4,004
2·2
4,620
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 0.3
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
2 4
4,000
2+2
4,005
2·2
4,059
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 1
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
2 4
4,000
2+2
4,004
2·2
4,620
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 3
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
2 4
4,131
2+2
4,372
2·2
4,977
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 1
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
2 4
4,000
2+2
4,004
2·2
4,620
x
Íå÷åòêèå îïåðàöèè
µA (x)
=
2 x−dAe
max 0, 1 −
K
K
= 1
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
4
4,000
2+2
4,005
2·2
4,392
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 1
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
2 4
4,000
2+2
4,004
2·2
4,620
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 1
T (x, y ) = min(x, y )
S(x, y ) = max(x, y )
µ
2 4
4,000
2+2
4,012
2·2
4,783
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 1
T (x, y ) = xy
S(x, y ) = max(x, y )
µ
2 4
4,000
2+2
4,004
2·2
4,620
x
Íå÷åòêèå îïåðàöèè
µA (x)
= exp
x−dAe
K
K
= 1
T (x, y ) = xy
S(x, y ) = x + y − xy
µ
2 4
4,000
2+2
4,074
2·2
4,979
x
Ðàçìûâàíèå
6
6,000
µ
x
Ðàçìûâàíèå
6
6,000
3+3
6,001
µ
x
Ðàçìûâàíèå
6
6,000
3+3
6,001
2 + 2 + 2 6,003
µ
x
Ðàçìûâàíèå
6
6,000
3+3
6,001
2 + 2 + 2 6,003
1+. . .+1 5,961
µ
x
Ðàçìûâàíèå
6
6,000
3+3
6,001
2 + 2 + 2 6,003
1+. . .+1 5,961
2·3
6,411
µ
x
Ðàçìûâàíèå
6
6,000
3+3
6,001
2 + 2 + 2 6,003
1+. . .+1 5,961
µ
2·3
6,411
6·1
5,415
x
Ðàçìûâàíèå
A+B
B
a+b
f (a, b) =
b
µC (c) =
max µA (a)µB (b)
C=
a,b f (a,b)=c
µ
x